Introduction To Probability Theory Important Questions

11th Standard

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Maths

Answer all the questions

Time : 01:40:00 Hrs
Total Marks : 50

    Part A

    10 x 1 = 10
  1. A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are\({3\over4},{1\over2},{5\over 8}\). The probability that the target is hit by A or B but not by C is

    (a)

    \({21\over64}\)

    (b)

    \({7\over32}\)

    (c)

    \({9\over64}\)

    (d)

    \({7\over8}\)

  2. A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

    (a)

    \({3\over 14}\)

    (b)

    \({5\over 14}\)

    (c)

    \({1\over 14}\)

    (d)

    \({9\over 14}\)

  3. If two events A and B are independent such that P(A)=0.35 and \(P(A\cup B)=0.6\) ,then P(B) is

    (a)

    \({5\over 13}\)

    (b)

    \({1\over 13}\)

    (c)

    \({4\over 13}\)

    (d)

    \({7\over 13}\)

  4. If m is a number such that m \(\le\) 5, then the probability that quadratic equation 2x2+2mx+m+1=0 has real roots is

    (a)

    \({1\over 5}\)

    (b)

    \({2\over 5}\)

    (c)

    \({3\over 5}\)

    (d)

    \({4\over 5}\)

  5. A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement is

    (a)

    \(\frac { 7 }{ 20 } \)

    (b)

    \(\frac { 13 }{ 20 } \)

    (c)

    \(\frac { 3 }{ 5 } \)

    (d)

    \(\frac { 2 }{ 5 } \)

  6. A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is

    (a)

    \(\frac { 64 }{ 64 } \)

    (b)

    \(\frac { 49 }{ 64 } \)

    (c)

    \(\frac { 40 }{ 64 } \)

    (d)

    \(\frac { 24 }{ 64 } \)

  7. If A and B are two events such that P(A) = \(\frac { 4 }{ 5 } \) and \(P(A\cap B)=\frac { 7 }{ 10 } \) then P(B/A) = 

    (a)

    \(\frac { 1 }{ 10 } \)

    (b)

    \(\frac { 1 }{ 8 } \)

    (c)

    \(\frac { 7 }{ 8 } \)

    (d)

    \(\frac { 17 }{ 20 } \)

  8. If P(A)=\(\frac { 1 }{ 2 } \), P(B)=\(\frac { 1 }{ 3 } \) and P(A/B) = \(\frac { 1 }{ 4 } \), then \(P(\bar { A } \cap \bar { B } )\) =

    (a)

    \(\frac { 1 }{ 12 } \)

    (b)

    \(\frac { 3 }{ 4 } \)

    (c)

    \(\frac { 1 }{ 4 } \)

    (d)

    \(\frac { 3 }{ 16 } \)

  9. If P(A) = 0.4, P(B) = 0.3 and P(AUB) = 0.5, then \(P(\bar { B } \cap A)\)

    (a)

    \(\frac { 2 }{ 3 } \)

    (b)

    \(\frac { 1 }{ 2 } \)

    (c)

    \(\frac { 3 }{ 10 } \)

    (d)

    \(\frac { 1 }{ 5 } \)

  10. A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is

    (a)

    \(\frac { 3 }{ 28 } \)

    (b)

    \(\frac { 1 }{ 14 } \)

    (c)

    \(\frac { 9 }{ 64 } \)

    (d)

    \(\frac { 33 }{ 56 } \)

  11. Part B

    5 x 2 = 10
  12. If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
    \(P(A)=\frac { 1 }{ \sqrt { 3 } } ,\quad P(B)-1-\frac { 1 }{ \sqrt { 3 } } ,\quad P(C)-0\)

  13. An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
    P(A) = 0.22 , P(B) = 0.38 , P(C) = 0. 16, P (D) = 0.34

  14. Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
    P(A∪B)

  15. The probability that student selected at random from a class will pass in Mathematics is \(\frac { 2 }{ 3 } \) and the probability that he passes in Mathematics and English is \(\frac { 1 }{ 3 } \). What is the probability that he will pass in English if it is known that he has passed in Mathematics?

  16. Given that the events A and B are such that P(A) = \(\frac { 1 }{ 2 } \), P(AUB) = \(\frac { 3 }{ 5 } \) and P(B) = p. find P if they are mutually exclusive events. 

  17. Part C

    5 x 3 = 15
  18. A problem in Mathematics is given to three students whose chances of solving A problem in Mathematics is given to three students whose chances of solving \(\frac { 1 }{ 3 } ,\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 5 } \) (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

  19. A firm manufactures PVC pipes in three plants viz, X, Y, and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units, and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production,
    (i) find the probability that the selected pipe is a defective one.
    (ii) if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

  20. The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
    (i) \(P(A\cup B)\)
    (ii) \(P(A\cap \bar { B } )\)
    (iii) \(P(\bar { A } \cap B)\)

  21. One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).

  22. A bag contains 10 white and 15 black balls. 2 balls are drawn in succession without replacement. What is the probability that first is white and second is black?

  23. Part D

    3 x 5 = 15
  24. If A and B are two independent events such that P(A\(\cup \)B)=0.6, P(A)=0.2,  find P(B).

  25. Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are Jack when the first drawn card is (i) replaced (ii) not replaced.

  26. Urn-I contains 8 red and 4 blue balls and urn-II contains 5 red and 10 blue balls. One urn is chosen at random and two balls are drawn from it. Find the probability that both balls are red.

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